Homework Assignment Three Linear Regression Each question is worth one point. The personnel director for

Homework Assignment Three

Linear Regression

Each question is worth one point.

The personnel director for a local manufacturing firm has received complaints from the employees in a certain shop regarding what they perceive to be inequities in the annual salary for employees who have similar performance ratings and years of service. The personnel director believes that an employee’s pay in this particular shop should be positively correlated to their prior performance ratings and years of service. The personnel director has collected the data shown in the following table pertaining to the employees within the shop.

Employee	Annual Salary	Avg Perf ormance Rating (5 -point Scale)	Years of Service
1	$56,100	3.9	10
2	$55,300	3.7	21
3	$48,600	2.4	19
4	$61,800	4.5	36
5	$56,400	3.9	31
6	$52,500	3.6	14
7	$52,600	3.6	25
8	$62,600	5.0	30
9	$45,100	3.1	8
10	$74,300	5.0	44
11	$53,200	3.7	23
12	$44,300	4.1	12
13	$55,300	3.8	19
14	$59,100	4.1	35
15	$60,000	4.2	39
16	$48,600	3.5	21
17	$50,400	3.5	11
18	$63,000	4.2	41
19	$53,000	3.7	35
20	$50,900	3.4	23

The personnel director is interested in creating a linear regression model that can be used to predict the annual salary an employee might expect to receive based upon his or her past performance and/or years of service. The regression model will be used as a basis for determining whether or not there is any validity to the employees’ complaints regarding salary inequities.

Perform a regression analysis for predicting an employee’s annual salary based upon his or her average performance rating for the past 3 years using a 95% confidence level. Use the results of this regression to answer questions 1 through 6.

What is the degree of correlation observed between the dependent variable and independent variable?
Does this model satisfy the desired statistical significance criteria for the model as a whole, and the desired statistical significance criteria for the linear relationship between the dependent and independent variables? Explain the basis for your answer.
What percentage of the observed variation between the actual values of the dependent variable and the mean value of the dependent variable in the sample data set is explained by this regression model? Explain the basis for selecting the specific regression statistic that you used to answer this question.
What is the regression formula associated with this model?
What is the predicted salary for an employee with an average performance rating of 3.9?
What is the amount by which the predicted salary for an employee will be off on average when using this regression model?

Perform each of the following additional regression analyses using a 95% confidence level.

Predicting an employee’s annual salary based upon years of service
Predicting an employee’s annual salary based upon average performance rating for the past 3 years and years of service

Calculate the degree of multicollinearity between the two independent variables and explain why the observed degree of multicollinearity does or does not render the model for predicting annual salary based upon average performance rating for the past 3 years and years of service unacceptable with regard to its statistical significance.
Based upon comparing the regression statistics for the three regression models, which of the three regression models would be considered the preferred regression model? Explain the basis for your answer.
Note: For the purposes of this question, the minimum difference between the R ² or Adjusted R ² values for acceptable models with differing numbers of independent variables that would favor selecting the model with the larger number of independent variables is 0.10.
What is the regression formula associated with the annual salary versus average performance rating and years of service regression model?
Based upon using the regression formula for the annual salary versus average performance rating and years of service regression model, what is the predicted salary for an employee with an average performance rating of 3.5 and 15 years of service?
Based upon using the regression formula for the annual salary versus average performance rating and years of service regression model, calculate the predicted salary for each employee and compare his or her predicted salary to his or her current annual salary. How many employees’ current annual salary is less than his or her predicted salary?
Based upon using the regression formula for the annual salary versus average performance rating and years of service regression model, calculate an interval estimate for the predicted salary for each employee based upon using his or her predicted salary ± the standard error for the regression model and compare the interval estimate for his or her predicted salary to his or her current annual salary.
How many employees’ current annual salary is below the lower limit for the interval estimate for his or her predicted salary?
How many employees’ current annual salary is above the upper limit for the interval estimate for his or her predicted salary?
Based upon using the 95% confidence level regression formulas for the annual salary versus average performance rating and years of service regression model, calculate an interval estimate for the predicted salary for each employee and compare the interval estimate for his or her predicted salary to his or her current annual salary.
How many employees’ current annual salary is below the lower limit for the 95% confidence level interval estimate for his or her predicted salary?
How many employees’ current annual salary is above the upper limit for the 95% confidence level interval estimate for his or her predicted salary?